Dynamics of Colombo’s top: tidal dissipation and resonance capture, with applications to oblique super-Earths, ultra-short-period planets and inspiraling hot Jupiters

We present a comprehensive theoretical study on the spin evolution of planet under combined effects tidal dissipation and gravitational perturbation from an external companion. Such "spin + companion" system (called Colombo's top) appears in many [exo]planetary contexts. The competition between torque (which drives spin-orbit alignment synchronization) companion orbital precession planet) gives rise to two possible equilibria ("Tidal Cassini Equilibria", tCE) that are stable attracting: "simple" tCE1, which typically has low obliquity, "resonant" tCE2, can have significant obliquity. latter arises resonance be broken when is stronger than precessional characterize long-term planetary (both magnitude obliquity) for arbitrary initial orientation, develop new method analytically obtain probability capture driven by dissipation. Applying our general results exoplanetary systems, we find super-Earth (SE) with exterior substantial being trapped high-obliquity assuming SEs wide range primordial obliquities. also evaluate recently proposed "obliquity tide" scenarios formation ultra-short-period Earth-mass planets decay hot Jupiter WASP-12b. both cases resonant into tCE2 generally such state easily required decay.